SOLUTION: I don't understand how to preform the operations with complex numbers like with; (6-5i)(4-9i) and also like; please help, I need to get my grade back to a B by tmoorrow... 2+3i/

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I don't understand how to preform the operations with complex numbers like with; (6-5i)(4-9i) and also like; please help, I need to get my grade back to a B by tmoorrow... 2+3i/       Log On


   



Question 694095: I don't understand how to preform the operations with complex numbers like with;
(6-5i)(4-9i) and also like; please help, I need to get my grade back to a B by tmoorrow...
2+3i/
4-5i

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(6-5i)(4-9i)
Use FOIL:
F: 6*4 = 24
O:6*-91 = -54i
I:-5i*4 = -20i
L:-5i*-9i = -45
------
Combine to get:
-21 -74i
====================
(2+3i)/(4-5i)
----
Multiply numerator and denominator by (4+5i) to get:
-----
= [(2+3i)(4+5i)]/[(4-5i)(4+5i)]
-------
= [8-15 + 21i+10i] / [16+25]
------
= [-7+31i]/41
=====================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
you have to know that
+i+=+sqrt%28-1%29+
+i%5E2+=+-1
------------
+i%5E3+=+i%2A%28-1%29+
+i%5E3+=+-i+
------------
+i%5E4+=+%28-1%29%2A%28-1%29+
+i%5E4+=+1+
-------------
To multiply +6+-+5i+%29%2A%28+4+-+9i+%29+, you need
to know the more basic operation
+%28+a+%2B+b+%29%2A%28+c+%2B+d+%29+=+a%2Ac+%2B+b%2Ac+%2B+a%2Ad+%2B+b%2Ad+
You're doing the same thing with operations on +i+
+6+-+5i+%29%2A%28+4+-+9i+%29+=+24+-+20i+-+54i+%2B+45%2Ai%5E2+
+6+-+5i+%29%2A%28+4+-+9i+%29+=+24+%2B+45%2A%28-1%29++-+20i+-+54i+
+6+-+5i+%29%2A%28+4+-+9i+%29+=+-21++-+74i+
---------------
+%28+2+%2B+3%2Ai+%29+%2F+%28+4+-+5%2Ai+%29+
Multiply top and bottom by +4+%2B+5%2Ai+


+%28+%28+2+%2B+3%2AI+%29%2A%28+4+%2B+5%2Ai+%29+%29+%2F+%28+16+-+25%2A%28i%5E2%29+%29+
+%28+8+%2B+12%2Ai+%2B+10%2Ai+%2B+15%2Ai%5E2+%29+%2F+%28+16+%2B+25+%29+
+%28+8+-+15+%2B+22i+%29+%2F+41+
+-7%2F41+%2B+%2822%2F41%29%2Ai+
----------------------
It's easy to make a mistake on these, but
I hope you get the idea